A023442 Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-12).

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 232, 375, 605, 977, 1577, 2546, 4110, 6635, 10711, 17291, 27913, 45060, 72741, 117426, 189562, 306011, 493996, 797461, 1287347, 2078173, 3354809, 5415691, 8742587

Offset

0,4

Links

Table of n, a(n) for n=0..35.

J. H. E. Cohn, Letter to the editor, Fib. Quart. 2 (1964), 108.

V. E. Hoggatt, Jr. and D. A. Lind, The dying rabbit problem, Fib. Quart. 7 (1969), 482-487.

Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: x/ ( (x-1)*(x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2-1) ). - R. J. Mathar, Nov 29 2011

Mathematica

LinearRecurrence[{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89}, 40] (* Harvey P. Dale, Aug 29 2021 *)

Prog

(PARI) concat(0, Vec(x/ ( (x-1)*(x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2-1) ) + O(x^50))) \\ Michel Marcus, Sep 06 2017

Crossrefs

See A000045 for the Fibonacci numbers.

Sequence in context: A023441 A268133 A217737 * A000044 A107358 A374266

Adjacent sequences: A023439 A023440 A023441 * A023443 A023444 A023445

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved